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Question
Expand the following:
`((2a)/(5b) - (5b)/(2a))^2`
Sum
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Solution
`((2a)/(5b) - (5b)/(2a))^2`
Let, `x = (2a)/(5b), y = (5b)/(2a)`
Thus,
`((2a)/(5b) - (5b)/(2a))^2 = ((2a)/(5b))^2 - 2((2a)/(5b) xx (5b)/(2a)) + ((5b)/(2a))^2` ...[Using (x − y)2 = x2 − 2xy + y2]
`((2a)/(5b) - (5b)/(2a))^2 = (4a^2)/(25b^2) - 2 xx (2a)/(5b) xx (5b)/(2a) + (25b^2)/(4a^2)`
∴ `((2a)/(5b) - (5b)/(2a))^2 = (4a^2)/(25b^2) - 2 + (25b^2)/(4a^2)`
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Chapter 3: Expansions - EXERCISE A [Page 32]
